if you didn't have the \(-10x\) you would have
\[\int cos(x)dx=\sin(x)\] because
\[\frac{d}{dx}[\sin(x)]=\cos(x)\] but
\[\frac{d}{dx}[\sin(-10x)]=-10\cos(-10x)\] by the chain rule therefore, to get what you want, you have to divide by \(-10\)